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Hypercube Graph

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  • Difficulty Level : Basic
  • Last Updated : 14 Sep, 2022
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You are given input as order of graph n (highest number of edges connected to a node), you have to find the number of vertices in a Hypercube graph of order n. 

Examples:  

Input : n = 3
Output : 8

Input : n = 2
Output : 4

In hypercube graph Q(n), n represents the degree of the graph. Hypercube graph represents the maximum number of edges that can be connected to a graph to make it an n degree graph, every vertex has the same degree n and in that representation, only a fixed number of edges and vertices are added as shown in the figure below:

Hypercube Graph

All hypercube graphs are Hamiltonian, hypercube graph of order n has (2^n) vertices, , for input n as the order of graph we have to find the corresponding power of 2.  

Recursive Approach

C++




// C++ program to find vertices in a hypercube
// graph of order n
#include <iostream>
using namespace std;
 
// function to find power of 2
int power(int n)
{
    if (n == 1)
        return 2;
    return 2 * power(n - 1);
}
 
// driver program
int main()
{
    // n is the order of the graph
    int n = 4;
    cout << power(n);
    return 0;
}

Java




// Java program to find vertices in
// a hypercube graph of order n
class GfG
{
 
    // Function to find power of 2
    static int power(int n)
    {
        if (n == 1)
            return 2;
        return 2 * power(n - 1);
    }
     
    // Driver program
    public static void main(String []args)
    {
         
        // n is the order of the graph
        int n = 4;
        System.out.println(power(n));
    }
}
 
// This code is contributed by Rituraj Jain

Python3




# Python3 program to find vertices in a hypercube
#  graph of order n
 
# function to find power of 2
def power(n):
    if n==1:
        return 2
    return 2*power(n-1)
 
 
# Driver code
n =4
print(power(n))
 
 
# This code is contributed by Shrikant13

C#




// C# program to find vertices in
// a hypercube graph of order n
using System;
 
class GfG
{
 
    // Function to find power of 2
    static int power(int n)
    {
        if (n == 1)
            return 2;
        return 2 * power(n - 1);
    }
     
    // Driver code
    public static void Main()
    {
         
        // n is the order of the graph
        int n = 4;
        Console.WriteLine(power(n));
    }
}
 
// This code is contributed by Mukul Singh

PHP




<?php
// PHP program to find vertices in
// a hypercube graph of order n
{
 
    // Function to find power of 2
    function power($n)
    {
        if ($n == 1)
            return 2;
        return 2 * power($n - 1);
    }
     
    // Driver Code
    {
         
        // n is the order of the graph
        $n = 4;
        echo(power($n));
    }
}
 
// This code is contributed by Code_Mech
?>

Javascript




<script>
 
 
// Javascript program to find vertices in a hypercube
// graph of order n
 
// function to find power of 2
function power(n)
{
    if (n == 1)
        return 2;
    return 2 * power(n - 1);
}
 
// driver program
// n is the order of the graph
var n = 4;
document.write( power(n));
 
</script>

Output

16

Iterative Approach

Java




/*package whatever //do not write package name here */
 
import java.io.*;
 
// Java program to find vertices in
// a hypercube graph of order n
class GFG {
   
  // Function to find power of 2
    static int power(int n)
    {
       
      if(n==0) return 0;
       
      int pow = 1;
       
      for(int i=1;i<=n;i++){
          pow *= 2;
      }
       
      return pow;
    }
   
    public static void main (String[] args) {
         // n is the order of the graph
        int n = 4;
        System.out.println(power(n));
    }
}

Output

16

Java Using Math.pow()

Java




/*package whatever //do not write package name here */
 
import java.io.*;
 
// Java program to find vertices in
// a hypercube graph of order n
class GFG {
   
  // Function to find power of 2
    static int power(int n)
    {
      return (int)Math.pow(2,n);
    }
   
    public static void main (String[] args) {
         // n is the order of the graph
        int n = 4;
        System.out.println(power(n));
    }
}

Output

16

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